View full sizeEzra Shaw/Getty ImagesThe Giants' Derrick Martin makes a video of head coach Tom Coughlin as he celebrates in the locker room after tonight's victory over the San Francisco 49ers in the NFC Championship Game at Candlestick Park.

SAN FRANCISCO — There was plenty to talk about after a night like this. He could have rhapsodized about the defense, which proved, once and for all, that it is the best in the NFL tonight. He could have gushed about the special teams, which came up with plays that resulted in 10 points and helped win the field-position tug-of-war. He could have thrown more rose petals at his quarterback, who took the hits and kept coming back for more, as boringly brilliant as he has become.

He could have even talked about the weather, because everyone still felt soaked by the 68-minute pelting they endured in the bog at Candlestick Point.

“Tom Coughlin deserves a lot of credit,” the Giants owner said, as he was pinned against a wall of a jubilant locker room. “Hopefully our fans and people in the New York and New Jersey area appreciate him a little more.”

Change the perceptions of New Yorkers and Jerseyans? It is to laugh.

“But I hope so,” Mara replied. “I mean, what more does he have to do? So I hope so.”

You look back at the last five weeks and still shake your head. How does a 7-7 team earn an all-expenses-paid trip to Indianapolis in two weeks? By having faith, is our guess. By listening to a remarkable, indomitable coach. At least that’s what the owner thinks.

His coach is a man who feels certitude when others feel doubt, even when there was a gong watch for his job back in Week 15 or so. Now, in the stunning aftermath of the Giants’ triumph, you have to wonder whether Coughlin himself is almost as stunned as the rest of us.

“How? By just staying the course. By never saying never. By trying to encourage at every point throughout the season, whether it was good or bad,” Coughlin explained. “Not denying any of the facts, but still nevertheless seeing that we had a talented team, believing in that team, thinking that if we could get all these pieces together that maybe we’d have a chance to make ourselves recognized.”

And somehow, it has evolved into his kind of team, playing his brand of football — if you just walked the field before this one, you’d understand it. You could hear an audible squish with each footstep. It was a grimy, sloppy mess, a game of precision played in a big gooey bog, and it made for an entertaining show if you happen to like defense.

As physics experiments go, this irresistible-force-vs.-immobile-object has been regarded by most scientists as a waste of time. Coughlin thought differently, of course: “A classic football game,” he said, more than once. “It looked like no one was going to put themselves in position to win.”

By the time the overtime began, the offensive line was slowly but surely starting to deteriorate like a two-ton block of papier-mache left out in a flood, the center snaps were starting to get a little slippery, and Eli Manning was starting to take some serious hits.

But something had to give, and as it turned out, it was 49ers return specialist Kyle Williams.

Coughlin predicted it: “We knew going in and we talked about it; it felt some (upstart) is going to be the difference-maker in the game,” the coach said, and that player ended up being gunner Devin Thomas.

So off they go, gunning the accelerator. Again, how does this happen? Five weeks after it seemed they were headed for the NFC East dumpster, after losing for the second time to the last-place Washington Redskins? Maybe they were inspired by the jowly foghorn from Florham Park, or maybe the team ahead of them in the standings decided it didn’t want to play anymore when its quarterback suffered a hand injury. Or maybe they just started to share the coach’s faith, judging by the way they smashed their next four opponents by an average count of 30-12.

Now comes Game 20. The NFL is happy, because it has a Manning-Brady matchup instead of (gasp) Flacco-Smith. The fans are happy, because it includes two enormously popular teams.

“I’m not surprised,” Coughlin said of reaching XLVI. “I’m delighted. I’m excited. But these guys have done it against the best. We’ve played a lot of superior teams this year, especially down the stretch, and that certainly has helped.”

Indeed, the Giants have to be very happy for a few reasons: They remember what happened back in Week 9 when the beat the Patriots, and they have made it abundantly clear what only Coughlin has told them for months now — that they are richly endowed in all the areas that separate the second weekend of December from the first week in February.

“We’re going to play our best game,” Justin Tuck said.

We don’t doubt it for a minute. Because they have a coach who will insist on nothing less.

“Nobody works harder than he does,” Mara said. “Nobody wants to win more than he does. And he knows how to win. Nobody could have predicted that we’d be here right now in early November, and Tom deserves most of the credit — he and No. 10.”

Coughlin himself could only laugh at it. He said Osi Umenyiora sidled up to him in the postgame tumult and nudged him, exulting, “Have you thought about the way this is coming down? Do you realize this is scary because of the way it’s coming about?”